Elliptic curves over $\Q$ of conductor 273999

Results (18 matches)

 

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
273999.a1	273999a1	273999.a	273999a	$1$	$1$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( - 3 \cdot 11 \cdot 19^{11} \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1254$	$2$	$0$	$2.700110647$	$1$		$2$	$13276800$	$2.202003$	$67837440610304/43225260243$	$0.90179$	$3.95458$	$[0, 1, 1, 306730, -20684020]$	\(y^2+y=x^3+x^2+306730x-20684020\)	1254.2.0.?	$[(1032, 37363)]$
273999.b1	273999b1	273999.b	273999b	$1$	$1$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( - 3 \cdot 11^{3} \cdot 19^{9} \cdot 23^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1254$	$2$	$0$	$2.388379413$	$1$		$0$	$9813120$	$2.624119$	$-12487168000/1117405113$	$0.93399$	$4.37632$	$[0, 1, 1, -331518, 916435880]$	\(y^2+y=x^3+x^2-331518x+916435880\)	1254.2.0.?	$[(14437/3, 1814192/3)]$
273999.c1	273999c1	273999.c	273999c	$1$	$1$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( - 3^{11} \cdot 11 \cdot 19^{9} \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1254$	$2$	$0$	$1.845536656$	$1$		$2$	$22239360$	$2.879097$	$-11168524389693952000/7070383357587$	$0.94601$	$4.91398$	$[0, 1, 1, -16811168, -26550581962]$	\(y^2+y=x^3+x^2-16811168x-26550581962\)	1254.2.0.?	$[(29323, 4969345)]$
273999.d1	273999d1	273999.d	273999d	$2$	$2$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( 3^{8} \cdot 11 \cdot 19^{3} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$19228$	$12$	$0$	$3.263007742$	$1$		$3$	$709120$	$1.223574$	$370192631098627/38178459$	$0.91275$	$3.38462$	$[1, 1, 1, -28422, -1855974]$	\(y^2+xy+y=x^3+x^2-28422x-1855974\)	2.3.0.a.1, 418.6.0.?, 1012.6.0.?, 1748.6.0.?, 19228.12.0.?	$[(1030, 32087)]$
273999.d2	273999d2	273999.d	273999d	$2$	$2$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( - 3^{16} \cdot 11^{2} \cdot 19^{3} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$19228$	$12$	$0$	$6.526015484$	$1$		$0$	$1418240$	$1.570147$	$-291210124287187/119799024543$	$0.91912$	$3.40834$	$[1, 1, 1, -26237, -2150512]$	\(y^2+xy+y=x^3+x^2-26237x-2150512\)	2.3.0.a.1, 836.6.0.?, 1012.6.0.?, 1748.6.0.?, 19228.12.0.?	$[(7379/5, 480373/5)]$
273999.e1	273999e1	273999.e	273999e	$1$	$1$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( 3^{2} \cdot 11 \cdot 19^{10} \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$44$	$2$	$0$	$10.49818585$	$1$		$0$	$3250368$	$2.198559$	$8713662409/52371$	$0.93262$	$4.17962$	$[1, 0, 0, -784641, -266191578]$	\(y^2+xy=x^3-784641x-266191578\)	44.2.0.a.1	$[(-281783/24, 14452423/24)]$
273999.f1	273999f5	273999.f	273999f	$6$	$8$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( 3 \cdot 11 \cdot 19^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$230736$	$192$	$1$	$16.50546522$	$1$		$0$	$7077888$	$2.587326$	$89254274298475942657/17457$	$1.00726$	$5.07989$	$[1, 1, 0, -33610551, 74986048896]$	\(y^2+xy=x^3+x^2-33610551x+74986048896\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 48.24.0.f.1, 66.6.0.a.1, $\ldots$	$[(87099923/154, 114477539709/154)]$
273999.f2	273999f3	273999.f	273999f	$6$	$8$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( 3^{2} \cdot 11^{2} \cdot 19^{6} \cdot 23^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$115368$	$192$	$1$	$8.252732613$	$1$		$2$	$3538944$	$2.240753$	$21790813729717297/304746849$	$0.97272$	$4.41558$	$[1, 1, 0, -2100666, 1170992295]$	\(y^2+xy=x^3+x^2-2100666x+1170992295\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0.h.1, 76.24.0.?, 88.24.0.?, $\ldots$	$[(9714/11, 42096933/11)]$
273999.f3	273999f6	273999.f	273999f	$6$	$8$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( - 3 \cdot 11 \cdot 19^{6} \cdot 23^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$230736$	$192$	$1$	$16.50546522$	$1$		$0$	$7077888$	$2.587326$	$-19989223566735457/2584262514273$	$0.97497$	$4.42479$	$[1, 1, 0, -2041101, 1240599954]$	\(y^2+xy=x^3+x^2-2041101x+1240599954\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0.by.1, 76.12.0.?, $\ldots$	$[(18602369/440, 2750100165723/440)]$
273999.f4	273999f4	273999.f	273999f	$6$	$8$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( 3^{2} \cdot 11^{8} \cdot 19^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$230736$	$192$	$1$	$2.063183153$	$1$		$0$	$3538944$	$2.240753$	$309368403125137/44372288367$	$0.95365$	$4.07577$	$[1, 1, 0, -508656, -121310451]$	\(y^2+xy=x^3+x^2-508656x-121310451\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0.by.2, 76.12.0.?, $\ldots$	$[(-1281/2, 25107/2)]$
273999.f5	273999f2	273999.f	273999f	$6$	$8$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( 3^{4} \cdot 11^{4} \cdot 19^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$115368$	$192$	$1$	$4.126366306$	$1$		$4$	$1769472$	$1.894180$	$5786435182177/627352209$	$0.98731$	$3.75798$	$[1, 1, 0, -135021, 17158680]$	\(y^2+xy=x^3+x^2-135021x+17158680\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0.h.2, 76.24.0.?, 88.24.0.?, $\ldots$	$[(1736, 69972)]$
273999.f6	273999f1	273999.f	273999f	$6$	$8$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( - 3^{8} \cdot 11^{2} \cdot 19^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$230736$	$192$	$1$	$8.252732613$	$1$		$1$	$884736$	$1.547606$	$3288008303/18259263$	$0.97810$	$3.33295$	$[1, 1, 0, 11184, 1339299]$	\(y^2+xy=x^3+x^2+11184x+1339299\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 46.6.0.a.1, 48.24.0.f.2, $\ldots$	$[(10594/5, 1108187/5)]$
273999.g1	273999g1	273999.g	273999g	$1$	$1$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( 3^{2} \cdot 11 \cdot 19^{4} \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$44$	$2$	$0$	$1.100921842$	$1$		$2$	$171072$	$0.726341$	$8713662409/52371$	$0.93262$	$2.76865$	$[1, 1, 0, -2173, 37894]$	\(y^2+xy=x^3+x^2-2173x+37894\)	44.2.0.a.1	$[(34, 52)]$
273999.h1	273999h2	273999.h	273999h	$2$	$2$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( 3^{5} \cdot 11^{4} \cdot 19^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$1.350120617$	$1$		$4$	$2280960$	$2.074707$	$209849322390625/1882056627$	$0.99362$	$4.04477$	$[1, 0, 1, -446926, 114068945]$	\(y^2+xy+y=x^3-446926x+114068945\)	2.3.0.a.1, 12.6.0.a.1, 92.6.0.?, 276.12.0.?	$[(421, 548)]$
273999.h2	273999h1	273999.h	273999h	$2$	$2$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( - 3^{10} \cdot 11^{2} \cdot 19^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$2.700241235$	$1$		$3$	$1140480$	$1.728132$	$-1349232625/164333367$	$0.95842$	$3.51760$	$[1, 0, 1, -8311, 4239749]$	\(y^2+xy+y=x^3-8311x+4239749\)	2.3.0.a.1, 12.6.0.b.1, 46.6.0.a.1, 276.12.0.?	$[(-143, 1655)]$
273999.i1	273999i1	273999.i	273999i	$2$	$2$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( 3^{8} \cdot 11 \cdot 19^{9} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$19228$	$12$	$0$	$1$	$1$		$1$	$13473280$	$2.695793$	$370192631098627/38178459$	$0.91275$	$4.79559$	$[1, 0, 1, -10260350, 12648041651]$	\(y^2+xy+y=x^3-10260350x+12648041651\)	2.3.0.a.1, 418.6.0.?, 1012.6.0.?, 1748.6.0.?, 19228.12.0.?	$[]$
273999.i2	273999i2	273999.i	273999i	$2$	$2$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( - 3^{16} \cdot 11^{2} \cdot 19^{9} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$19228$	$12$	$0$	$1$	$1$		$0$	$26946560$	$3.042366$	$-291210124287187/119799024543$	$0.91912$	$4.81931$	$[1, 0, 1, -9471565, 14674588073]$	\(y^2+xy+y=x^3-9471565x+14674588073\)	2.3.0.a.1, 836.6.0.?, 1012.6.0.?, 1748.6.0.?, 19228.12.0.?	$[]$
273999.j1	273999j1	273999.j	273999j	$1$	$1$	\( 3 \cdot 11 \cdot 19^{2} \cdot 23 \)	\( - 3 \cdot 11^{3} \cdot 19^{3} \cdot 23^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1254$	$2$	$0$	$1$	$1$		$0$	$516480$	$1.151899$	$-12487168000/1117405113$	$0.93399$	$2.96535$	$[0, -1, 1, -918, -133321]$	\(y^2+y=x^3-x^2-918x-133321\)	1254.2.0.?	$[]$